| Topic Name: |
Brainteaser |
| Message Name: |
The correct answer |
| Date Posted: |
01/09/2002 |
| In Reply To: |
The answer is prisoner 3, who is wearing a black hat. He knows this because prisoners 1 and 2 can not answer.
Prisoner 1 can see 2 (wearing red) and 3 (wearing black). Thus prisoner 1 can not work out the colour of his own hat. Similarly prisoner 2 can see 1 (wearing red) and 3 (wearing black) and again cannot work out the colour of his own hat. Prisoners 1 and 2 must be wearing the red hats as neither is able to answer. As there are only two red hats, prisoner 3 can rightly state he is wearing a black hat. |
| Message: |
The answer is of course black. But the logic should be explained in a differen manner.
There are seven possible combinations for prisoners represented 1,2,3 and I would divide them in two groups:
Group One
BBB, RRB, BRB,RBB
Group Two
RBR, BRR, BBR.
The answers in group one give us black for the third prisoner.
We just need to eliminate combinations in Group Two.
Combination RBR we exclude since the 2nd prisoner would have guessed it and shouted yes. Combination BRR we also exclude since prisoner #1 would have guessed it and shouted yes. Combination BBR we exclude because based on the negative answer of Prisoner #1, Prisoner # 2 assumes he must be black.
So, we exclude three combinations and are left with only those that give us black for Prisoner # 3.
Cheers,
Aleksander
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